This works is organised as follows. We first review the basic of warm inflation, the dissipative coefficient and background evolution for the interaction pattern with light scalar dof [1]} in Section II. In Section III we give the analytical expression of the growing mode for different constant values of \(\kappa \) . While this can be found in the literature for \(\kappa _*=3,\,1,\,-1\)  [2]}, [3]}, [4]}, [1]}, here we will generalize those results to other intermediate values. This will allow us to get the scalar primordial spectrum over the full range of inflation, and obtain the predictions for the scalar spectral index \(n_s\)  and the tensor-to-scalar ratio \(r\) . We comment also on the implications for PBHs at the end of Section III, and in Section IV we present the results for the spectrum of GW today. Finally, in section V we summarise and discuss our results.
